Abstract
Driftlessification is a novel technique to drive a nonlinear system towards a target state under input constraints. The core of the technique revolves around a linear driftless approximation to the original nonlinear system, constructed only using the effect of the control input at the initial state. Optimal controllers for this 'proxy' system are easily derived, and in fact lead to bounded error over a finite horizon in the original nonlinear system. The key step is then to partition the time horizon into successively shorter intervals, and we prove that as intervals become shorter, the error converges monotonically to zero. Simultaneously, we derive conditions on this partition which ensure the input constraint will be satisfied. A number of examples on classical nonlinear systems show the performance of this method, comparing favorably to other nonlinear control techniques, even when assumptions of the underlying theory are violated.
Performance Comparison with Nonlinear MPC
Driftlessification utilizes lower cumulative energy compared to nonlinear MPC.
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BibTeX
@article{driftlessification2025,
title={Ignore Drift, Embrace Simplicity: Constrained Nonlinear Control through Driftless Approximation},
author={Ram Padmanabhan and Melkior Ornik},
year = {2025},
eprint = {2509.06188},
archivePrefix = {arXiv},
primaryClass = {math.OC},
url = {https://arxiv.org/abs/2509.06188}
}